iamlost has got the answer (nice work!), and it doesn't look to good for Opera Software. So, if I've got it right (please correct me if I'm wrong on any of this):
Opera hacked their browser to send out a user agent string declaring itself as Netscape 4.78 just to the Wells Fargo site rather than the usual one as a quick fix to a bug in an earlier version of the WF site.
Their "patch" to get round Wells Fargo's bad browser-sniffing code has now backfired as the fake user agent string is now the cause for the blocking rather than the solution.
It is Netscape 4 which is being blocked, not Opera, which would get through if it wasn't for the earlier hack.
<added>In fact I'm partly wrong: Opera is still blocked, see later message!</added>
So who's to blame? Wells Fargo certainly for some poor browser-sniffing and a narrow-minded approach to browser compatibility, but also Opera Software must take responsibility for the ad-hoc "patch" which is now causing so much trouble.
[edited by: encyclo at 1:58 am (utc) on Feb. 3, 2005]